This is a huge part of answering this question because there are actually two different categories when speaking of prophecy. There is "Prophecy" and there is "prophecy".
In the Old Testament, there were men called Prophets who spoke the very words of God. They would say things like "Thus saith the Lord..." In fact, they wrote down the words that they spoke and their writings became part of the Bible and we treat them with God's authority to this day. These are men like Moses, Isaiah, Jeremiah, Ezekiel, Daniel, and others. In the New Testament, we see men who did similar things. We call them Apostles. This includes Peter, James, John, Paul, and others.
This kind of Prophecy (upper case P) is fully authoritative, 100% accurate, and always to be obeyed. This kind of Prophecy produces Scripture. This kind of Prophecy can be defined as "Declaring the very Words of God."
Throughout the Bible, we see a sort of lesser form of prophecy. We see people who speak under the guidance of the Holy Spirit. They declare praise to God and give counsel to those who need it. They sometimes received knowledge or insight that was beyond what they could have naturally known. These men and women are often nameless throughout the Bible but include men like King Saul and the disciples in Tyre mentioned in Acts 21:4.
This kind of prophecy (lower case p) is subject to the Scriptures. It is to be tested and weighed rather than accepted and obeyed. It does not produce Scripture. This kind of prophecy can be defined as "Speaking about something that God has revealed to you or called to your mind."